Question 1046879
.
A boat travels 80 km downstream in 2.5 hours. It travels 50 km upstream in the same length of time. 
what is the speed of the boat in still water and of the current?
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<pre>
For the trip downstream, your first equation is 

{{{80/2.5}}} = u + v,  or 

32 = u + v.   (1)

The term in the left side is the speed of the boat (relative to the bank of the river) on the trip downstream with the river current.
Here u is the boat speed in still water and v is the current speed.


For the upstream trip, your second equation is 

{{{50/2.5}}} = u - v,  or 

20 = u - v.   (2)

The term in the left side is the speed of the boat (relative to the bank of the river) on the trip upstream against the river current.
Again, here u is the boat speed in the still water and v is the current speed.


Rewrite the equations (1) and (2) in this way:

u + v = 32,   (3)
u - v = 20.   (4)

To solve them, add equations (3) and (4)  (both sides). You ill get

2u = 32 + 20,  or  2u = 52.  Hence,  u = {{{52/2}}} = 26.

You just found the speed of the boat in still water. It is 26 mph.

Now from (3)  v = 32 - u = 32 - 26 = 6.

Thus the current rate is 6 mph.

<U>Answer</U>.  The speed of the boat in still water is 32 mph.  The current rate is 6 mph.
</pre>

For many other solved problems on upstream and downstream trips see the lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Wind-and-Current-problems.lesson>Wind and Current problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/More-problems-on-upstream-and-downstream-round-trips.lesson>More problems on upstream and downstream round trips</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Selected-problems-from-the-archive-on-a-boat-floating-Upstream-and-Downstream.lesson>Selected problems from the archive on the boat floating Upstream and Downstream</A> 


Read them attentively and learn how to solve this type of problems once and for all.


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.